University applicants were yesterday told of an unprecedented squeeze on degree places with nearly 50,000 too few spaces available for this autumn, triggering warnings that Labour's decade-long drive to make higher education less elitist will be undermined unless more money is found to expand universities.

Applications to universities surged by nearly 10% in the past year, fuelled partly by rising numbers of older people applying to do a degree in the recession. There are 52,000 extra people attempting to get a full-time place at university this year but only 3,000 extra spaces in English institutions, after the government capped the number to avoid a cash crisis.

Ministers are now working on emergency plans to increase places by 10,000 to ease the looming crisis, but universities could veto the moves after they were told they may not get extra government funding for the students. Student leaders, vice-chancellors and the government's watchdog charged with ensuring fair access to universities all warned that some students could miss out in the squeeze this year.

The universities admissions service, Ucas, yesterday confirmed that there has been an increase in applications of 9.7% compared with the same point in the applications cycle last year. So far this year, 592,312 people have applied to universities to start courses this autumn, compared with 540,108 in July last year. The rate of growth in applications is higher among mature students than school leavers, with a 14.9% increase in the proportion of applicants aged 21 to 24, and an 18.8% increase from applicants over the age of 25.

There have been disproportionately high increases in applications to study nursing, hospitality, engineering and courses combining sciences and languages, indicating that students are now looking to gain hard skills at university. Applications to economics courses also increased by 13.8%.

Most university places will be filled when A-level results are announced, leaving very few places left for students to get through clearing, the system for allocating leftover places. Some universities are now warning there will be just 16,000 places in clearing, compared with 43,000 last year.

The cap on numbers was introduced to help ease a £200m black hole in the university budget discovered at the end of last year. Vice-chancellors were also told they face fines if they over-recruit. There are now concerns that admissions offices have been conservative in their offers to avoid incurring the fines, meaning they could in fact end up inadvertently under-recruiting, so even more would-be students miss out.

There are also fears that the competition could force out students from the poorest areas of the country, the very ones the government is trying to attract.

Sir Martin Harris, director of the Office for Fair Access (Offa), said: "It will be very important to ensure that applications from lower income families and other under-represented groups are not disproportionately affected by the increased demand for places this autumn."

He said the rise in applications resulted from the efforts of universities to encourage applications from lower income families, adding: "It would be an enormous waste if these efforts were set back just when they are starting to bear real fruit."

Wes Streeting, the NUS president, called on the government to fund more places. "We understand the current pressures on public finances, but the government must also make the right long-term decisions. It is surely better to bear the cost of increasing opportunities in education and training now than to shoulder the burden of long-term unemployment later."

David Lammy, the higher education minister, said: "There are record numbers of students currently in higher education – 300,000 more than in 1997. And this year we expect that there will be 40,000 more accepted applicants than just three years ago.

"Students who get the grades to meet their offer will secure a place at university this summer, but we will continue to work with the sector to support those who do not, and to manage increased demand."